Hello @MajoY ...
I just tested this in my own Canvas environment using two dummy accounts, Frodo Baggins and Optimus Prime. I found a past message in my Canvas Inbox between me and Optimus Prime. I forwarded the message I had received from Optimus Prime to Frodo Baggins. I then logged in as Frodo Baggins (I am a Canvas administrator at our Technical College, so I can do this). I was able to see the message I forwarded in Frodo's Inbox. I then logged in as Optimus. The message I forwarded to Frodo did not appear in Optimus' Inbox. So, to answer your question, it appears that a user would not be notified if you forwarded their message in your Inbox to another user.
Hope this helps a bit. Let Community members know if you have any other questions...thanks! Take care, stay safe, and be well.
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